Question: Solve for $x$ and $y$ using elimination. $\begin{align*}-8x+2y &= -2 \\ -4x-4y &= 4\end{align*}$
Solution: We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $2$ and the bottom equation by $1$ $\begin{align*}-16x+4y &= -4\\ -4x-4y &= 4\end{align*}$ Add the top and bottom equations. $-20x = 0$ Divide both sides by $-20$ and reduce as necessary. $x = 0$ Substitute $0$ for $x$ in the top equation. $-8( 0)+2y = -2$ $2y = -2$ $2y = -2$ $y = -1$ The solution is $\enspace x = 0, \enspace y = -1$.